User Ubik

2 votes

0 answers

76 views

Counter-example of continuous Z-periodic functions

asked Feb 6, 2023 at 18:36

2 votes

1 answer

98 views

Alternative proof for Structure theorem for finitely generated modules over a principal ideal domain

asked Sep 14, 2023 at 9:42

2 votes

0 answers

94 views

Can polynomial rings be classified as a specific type of ring like algebraic integers are classified as Dedekind domains??

asked Nov 20, 2023 at 22:00

1 vote

1 answer

86 views

If $A$ is absolutely flat, so is $S^{-1}A$ (A&M, Problem 3.10)

asked Aug 8, 2023 at 6:18

1 vote

2 answers

73 views

Asympototic estimation of log log function

asked Dec 5, 2023 at 16:37

1 vote

1 answer

176 views

If $M$ is a finitely generated module over a local ring, then $M$ is free.

asked Dec 15, 2023 at 21:26

1 vote

1 answer

55 views

Unique unramified ideal implies that the ramification index is equal to the degree of field extension in a galois extension

asked Feb 1 at 21:06

1 vote

0 answers

36 views

Flat base change preserves the non-degeneracy (Proposition 9.2 in Commutative Algebra, Matsumura)

asked Mar 26 at 22:00

1 vote

1 answer

58 views

$\text{depth }A\leq \text{depth }_{\frak{p}}A + \dim(A/{\frak{p}})$, where $A$ is a Noetherian local ring.

asked May 9 at 17:07

1 vote

0 answers

44 views

Homology group of an attaching space

asked Jun 10 at 12:08

1 vote

0 answers

58 views

Finding a surjective continuous map from $S^n$ to $T^n$, the $n$-torus

asked Jun 11 at 18:18

0 votes

0 answers

33 views

Understanding cellular boundary formula

asked Jun 15 at 13:46

0 votes

0 answers

13 views

Closedness in the component of a finite open cover implies closedness [duplicate]

asked Aug 27 at 10:00

0 votes

1 answer

274 views

Percolation theory: Proving that the critical probability is a non decreasing function of the dimension

asked Dec 13, 2022 at 16:30

0 votes

0 answers

55 views

Existence of an algebraic closure by Zorn's lemma

asked Aug 7, 2023 at 9:21

0 votes

1 answer

78 views

Applying Zorn's lemma to Cantor set

asked Nov 27, 2023 at 21:10

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16 Questions

Counter-example of continuous Z-periodic functions

Alternative proof for Structure theorem for finitely generated modules over a principal ideal domain

Can polynomial rings be classified as a specific type of ring like algebraic integers are classified as Dedekind domains??

If $A$ is absolutely flat, so is $S^{-1}A$ (A&M, Problem 3.10)

Asympototic estimation of log log function

If $M$ is a finitely generated module over a local ring, then $M$ is free.

Unique unramified ideal implies that the ramification index is equal to the degree of field extension in a galois extension

Flat base change preserves the non-degeneracy (Proposition 9.2 in Commutative Algebra, Matsumura)

$\text{depth }A\leq \text{depth }_{\frak{p}}A + \dim(A/{\frak{p}})$, where $A$ is a Noetherian local ring.

Homology group of an attaching space

Finding a surjective continuous map from $S^n$ to $T^n$, the $n$-torus

Understanding cellular boundary formula

Closedness in the component of a finite open cover implies closedness [duplicate]

Percolation theory: Proving that the critical probability is a non decreasing function of the dimension

Existence of an algebraic closure by Zorn's lemma

Applying Zorn's lemma to Cantor set